Question: Solve the system of equations. $\begin{aligned} &5x-7y= 58 \\\\ &y=-x+2 \end{aligned}$ $x=$
We are given that $ y = {-x+2}$. Let's substitute this expression into the first equation and solve for $x$ as follows: $ \begin{aligned} 5x-7{y}&=58\\\\ 5x-7\cdot({-x+2})&=58\\\\ 5x+7x-14& = 58\\\\ 12x&=72\\\\ x&=6 \end{aligned}$ Since we now know that $ x={6}$, we can substitute this value into the second equation to solve for $y$ as follows: $\begin{aligned} y &= - {x}+2 \\\\ y&=-{6}+2\\\\ y&=-4 \end{aligned}$ This is the solution of the system: $\begin{aligned} &x = 6 \\\\ &y=-4 \end{aligned}$